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2 years ago

Complete the sentence below. If (3x2 + 22x + 7) ÷(x + 7) = 3x + 1, then (x + 7)(???????) =???? .

Mathematics

2 answers:

g100num [7]2 years ago

7 0

Answer: The answer is $(x+7)(3x+1)=33x^2+22x+7.$

Step-by-step explanation: Given that

$(3x2 + 22x + 7) \div(x + 7) = 3x + 1,$

and we are to complete the following sentence:

$(x+7)(???)=???$

We have the following division algorithm for polynomials

$\textup{If }a(x)\times b(x)=c(x),\\\textup{then, we have }\\\\\dfrac{c(x)}{b(x)}=a(x)~~~~~\textup{or}~~~~~~c(x)\div b(x)=a(x).$

Here, a(x) = quotient, b(x) = divisor and c(x) = dividend.

Applying this rule in the given problem, we have

$\textup{since }(3x2 + 22x + 7) \div(x + 7) = 3x + 1,\\\\\textup{so, }\\\\(x+7)(3x+1)=3x^2+22x+7=0.$

Thus, the complete sentence is

$(x+7)(3x+1)=3x^2+22x+7=0.$

svetoff [14.1K]2 years ago

3 0

Answer:

3x+1, 3x^2+22x+7, and closure

Step-by-step explanation:

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Brian buys a computer for £4300. It depreciates at a rate of 3% per year. How much will it be worth in 6 years? Give your answer

aalyn [17]

Answer:

3526

Step-by-step explanation:

4300×3%=129

129×6=774

4300_774= 3526

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2 years ago

Read 2 more answers

−12x−5y=40 12x−11y=88 x= y=

Nezavi [6.7K]

Add the two equations and use the elimination method. The x term will "cancel out" to be able to solve for the y term.

STEP 1
−12x−5y=40
12x−11y=88
x terms "cancels out"; add y terms

-16y= 128
divide both sides by -16

y= -8

STEP 2
substitute y value into either original equation

12x−11y=88

12x - 11(-8)= 88

12x + 88= 88
subtract 88 from both sides

12x= 0
divide both sides by 12; 0 divided by any number is 0

x= 0

ANSWER: x= 0; y= -8

Hope this helps! :)

6 0

2 years ago

Shelley is searching online for airline tickets. Two weeks ago, the cost to fly from Boston to Denver was $300. Now the cost i

Nady [450]

Answer:

The percentage increase without baggage fee=25%

The percentage increase with baggage fee=41.66%

Step-by-step explanation:

Given the cost of the airline ticket two weeks ago is $300 and The present airline ticket is $375

We know that when a quantity increases from x to y then The percentage increase is equal to $\frac{y-x}{x} *100$

Here the percentage increase = $\frac{375-300}{300} *100$ =25%

Now the airline charges an extra $50 baggage fee which means teh present value of the airline ticket is $375+$50=$425

the percentage increase = $\frac{425-300}{300} *100$ =41.66%

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2 years ago

The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.6 minutes and a s

Rus_ich [418]

Answer:

37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 12.6, \sigma = 2.5$